Any suggestions on improving it? I was thinking of replacing the documents with actual session transcripts and more in depth descriptions of the D personnel going from well-adjusted to suicidal to give it a bit more impact. Or do you feel the core concept just doesn't have enough there to be of interest?

While it's not poorly written, this is also not really breaking any new ground. It's something that crazies you to death. There are a number of other SCPs that make people depressed, make people hurt themselves, make people kill themselves, redirect attempted injuries onto the user…

Maybe you should try hiding some of what it does, make it a touch more mysterious.

Or it was used in assassinations/executions, so the last person to handle the gun is found dead, with the appropriate gun shot wound, maybe to the back of the head.
Or the perceived enemy/rival of the last person to hold the gun is found dead.
And it is found near the body with the bloody fingerprint of the last person to hold it.
It frames you for murder, not particularly creepy, but what can you do?

One thing, under the Discovery section you have the words 'apparent homicide' followed in the next sentence by 'apparent murder weapon'.
I would replace one of those apparents with a synonym.
Maybe 'supposed murder weapon'.

Hmmm….guess I kind of hoped that the item's determination to return to the last owner and be sure they finished the job, so to speak, was enough of a variation on similar items. I'll keep working at it.

What if I added a sort of implied sentience to the gun? Replace the existing addendum with some further testing and experiments where it begins behaving more erratically and not following its established behaviors. Misfiring, escaping its containment and showing up in the possession of people who have not interacted with it, things like that.